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Search: id:A002418
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| A002418 |
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4-dimensional figurate numbers: (5*n-1)*binomial(n+2,3)/4.
(Formerly M4617 N1970)
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+0
7
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| 0, 1, 9, 35, 95, 210, 406, 714, 1170, 1815, 2695, 3861, 5369, 7280, 9660, 12580, 16116, 20349, 25365, 31255, 38115, 46046, 55154, 65550, 77350, 90675, 105651, 122409, 141085, 161820, 184760, 210056, 237864, 268345, 301665, 337995
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Partial sums of A002413.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 195.
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LINKS
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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.
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FORMULA
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G.f.: x*(1+4*x)/(1-x)^5.
Starting (1, 9, 35, 95,...), = A128064 * A000332, (A000332 starting 1, 5, 15, 35, 70,...), such that a(n) = n*C((n+3),4)) - (n-1)*C((n+2),4)). E.g. a(5) = 210 = 5*C(8,4) - 4*C(7,4) = 5*70 - 4*35. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2007
Unit digit, A010879(a(n)), is one of {0,1,9,5,6,4} [Eric Desbiaux] because a(n) mod 5 = 0,1,4,0,0, periodic with period 5. [Proof: A002413(n) mod 5 = 1,3,1,0,0 with period 5 and a(n) are the partial sums of A002413.] - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008
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MAPLE
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A002418:=-(1+4*z)/(z-1)**5; [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A093562 ((5, 1) Pascal, column m=4).
Cf. A128064, A000332.
Sequence in context: A071398 A005898 A034957 this_sequence A118414 A137628 A020297
Adjacent sequences: A002415 A002416 A002417 this_sequence A002419 A002420 A002421
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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