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A055268
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a(n) = (11*n + 4)*C(n+3, 3)/4.
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4
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1, 15, 65, 185, 420, 826, 1470, 2430, 3795, 5665, 8151, 11375, 15470, 20580, 26860, 34476, 43605, 54435, 67165, 82005, 99176, 118910, 141450, 167050, 195975, 228501, 264915, 305515, 350610, 400520, 455576, 516120, 582505, 655095, 734265
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of compositions of n when there are 9 types of each natural number. - Milan Janjic, Aug 13 2010
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.
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LINKS
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FORMULA
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a(n) = 11*binomial(n+4,4) - 10*binomial(n+3,3).
E.g.f.: (24 + 336*x + 432*x^2 + 136*x^3 + 11*x^4)*exp(x)/24. (End)
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MAPLE
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seq( (11*n+4)*binomial(n+3, 3)/4, n=0..30); # G. C. Greubel, Jan 17 2020
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MATHEMATICA
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Table[11*Binomial[n+4, 4] -10*Binomial[n+3, 3], {n, 0, 30}] (* G. C. Greubel, Jan 17 2020 *)
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PROG
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(Python)
A055268_list, m = [], [11, 1, 1, 1, 1]
for _ in range(10**2):
for i in range(4):
(PARI) a(n) = (11*n+4)*binomial(n+3, 3)/4; \\ Michel Marcus, Sep 07 2017
(Sage) [(11*n+4)*binomial(n+3, 3)/4 for n in (0..30)] # G. C. Greubel, Jan 17 2020
(GAP) List([0..30], n-> (11*n+4)*Binomial(n+3, 3)/4 ); # G. C. Greubel, Jan 17 2020
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CROSSREFS
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Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the k-gonal numbers.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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