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Search: id:A000566
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| A000566 |
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Heptagonal numbers (or 7-gonal numbers) n(5n-3)/2.
(Formerly M4358 N1826)
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+0
81
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| 0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970, 1071, 1177, 1288, 1404, 1525, 1651, 1782, 1918, 2059, 2205, 2356, 2512, 2673, 2839, 3010, 3186, 3367, 3553, 3744, 3940, 4141, 4347, 4558, 4774, 4995, 5221, 5452, 5688
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of (0,1,5,0,0,0,...) Binomial transform is A084899. - Paul Barry (pbarry(AT)wit.ie), Jun 10 2003
Also the partial sums of A016861, a zero added in front; therefore a(n) = n (mod 5). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189.
L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 2.
B. S. Rao, Heptagonal numbers in the Pell sequence and diophantine equations 2x^2 = y^2(5y-3)^2 +- 2, Fib. Quarterly, 43 (2005), 194-201.
B. S. Rao, Heptagonal numbers in the associated Pell sequence ..., Fib. Quarterly, 43 (2005), 302-306.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 341
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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G.f.: x(1+4x)/(1-x)^3; a(n)=C(n, 1)+5C(n, 2). - Paul Barry (pbarry(AT)wit.ie), Jun 10 2003
a(n)=sum{k=1..n, 4n-3k}. - Paul Barry (pbarry(AT)wit.ie), Sep 06 2005
a(n)=n+5*A000217(n-1) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 14 2005
Row sums of triangle A131413 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 08 2007
Sequence starting (1, 7, 18, 34,...) = binomial transform of (1, 6, 5, 0, 0, 0,...). Also row sums of triangle A131896. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 24 2007
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MAPLE
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A000566:=-(1+4*z)/(z-1)**3; [S. Plouffe in his 1992 dissertation.]
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+5 od: seq(a[n], n=0..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008
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CROSSREFS
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Cf. A014637, A014640, A014773, A014792, A069099.
a(n)= A093562(n+1, 2), (5, 1)-Pascal column.
Cf. A131413.
Cf. A131896.
Cf. A134483.
Cf. A000217, A000384, A000567.
Adjacent sequences: A000563 A000564 A000565 this_sequence A000567 A000568 A000569
Sequence in context: A103572 A049532 A033537 this_sequence A133673 A023166 A002764
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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