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Search: id:A086020
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| A086020 |
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a(n) = Sum_(i=1..n) C(i+2,3)^2 [ Sequential sums of the tetragonal numbers or "tetras" (pyramidal, square) raised to power 2 (drawn from the 4th diagonal - left or right - of the Pascal's Triangle) ]. |
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+0
24
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| 1, 17, 117, 517, 1742, 4878, 11934, 26334, 53559, 101959, 183755, 316251, 523276, 836876, 1299276, 1965132, 2904093, 4203693, 5972593, 8344193, 11480634, 15577210, 20867210, 27627210, 36182835, 46915011, 60266727, 76750327
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Kekule numbers for certain benzenoids (see the Cyvin-Gutman reference, p. 243; expression in (13.26) yields same sequence with offset 0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2005
Partial sums of A001249. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 19 2008]
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REFERENCES
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S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to linear recurrences with constant coefficients
A.F. Labossiere, New Artefact From Pascal's Triangle.
A.F. Labossiere, Miscellaneous.
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FORMULA
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Sum_(i=1..n) C(i+2, 3)^2 = [ C(n+3, 4)/35 ]*[ 35 +84*C(n-1, 1) +70*C(n-1, 2) +20*C(n-1, 3) ]
a(n)=n(n+1)(n+2)(n+3)(2n+3)(5n^2+15n+1)/2520. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2005
O.g.f: x(1+x)(1+8x+x^2)/(1-x)^8. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 19 2008]
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EXAMPLE
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a(8) = Sum_(i=1..8) C(i+2,3)^2 = [ 20*(8^7) +210*(8^6) +854*(8^5) +1680*(8^4)
+1610*(8^3) +630*(8^2) +36*8 ]/7! = 26334
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MAPLE
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a:=n->n*(n+1)*(n+2)*(n+3)*(2*n+3)*(5*n^2+15*n+1)/2520: seq(a(n), n=1..31); (Deutsch)
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PROGRAM
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Lotus version 2.01 - 1986 (spreadsheet)
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CROSSREFS
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Cf. A000292, A087127, A024166, A024166, A085438, A085439, A085440, A085441, A085442, A000332, A086021, A086022, A000389, A086023, A086024, A000579, A086025, A086026, A000580, A086027, A086028, A027555, A086029, A086030.
Sequence in context: A032692 A044349 A044730 this_sequence A056117 A003109 A066607
Adjacent sequences: A086017 A086018 A086019 this_sequence A086021 A086022 A086023
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Andre F. Labossiere (boronali(AT)laposte.net), Jul 17 2003
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 02 2005
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