A051878 Partial sums of A051797.
1, 13, 63, 203, 518, 1134, 2226, 4026, 6831, 11011, 17017, 25389, 36764, 51884, 71604, 96900, 128877, 168777, 217987, 278047, 350658, 437690, 541190, 663390, 806715, 973791, 1167453, 1390753, 1646968, 1939608, 2272424, 2649416, 3074841, 3553221, 4089351, 4688307, 5355454, 6096454
Offset: 0
References
- A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
- Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.
Links
- Index to sequences related to pyramidal numbers
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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GAP
List([0..40], n-> (8*n+5)*Binomial(n+4,4)/5); # G. C. Greubel, Aug 30 2019
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Magma
[(8*n+5)*Binomial(n+4,4)/5: n in [0..40]]; // G. C. Greubel, Aug 30 2019
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Maple
seq((8*n+5)*binomial(n+4,4)/5, n=0..40); # G. C. Greubel, Aug 30 2019
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Mathematica
Table[(8*n+5)*Binomial[n+4,4]/5, {n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011, modified by G. C. Greubel, Aug 30 2019 *) -
PARI
vector(40, n, (8*n-3)*binomial(n+3,4)/5) \\ G. C. Greubel, Aug 30 2019
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Sage
[(8*n+5)*binomial(n+4,4)/5 for n in (0..30)] # G. C. Greubel, Aug 30 2019
Formula
a(n) = binomial(n+4, 4)*(8*n+5)/5.
G.f.: (1+7*x)/(1-x)^6.
E.g.f.: (120 +*1440*x +2280*x^2 +1040*x^3 +165*x^4 +8*x^5)*exp(x)/120. - G. C. Greubel, Aug 30 2019
Extensions
Terms a(28) onward added by G. C. Greubel, Aug 30 2019
Comments