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

0,2

Comments

Convolution of triangular numbers (A000217) and decagonal numbers (A001107). [Bruno Berselli, Jul 21 2015]

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

Table of n, a(n) for n=0..37.

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

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

Maple

seq((8*n+5)*binomial(n+4, 4)/5, n=0..40); # G. C. Greubel, Aug 30 2019

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 *)

Prog

(PARI) vector(40, n, (8*n-3)*binomial(n+3, 4)/5) \\ G. C. Greubel, Aug 30 2019
(Magma) [(8*n+5)*Binomial(n+4, 4)/5: n in [0..40]]; // G. C. Greubel, Aug 30 2019
(Sage) [(8*n+5)*binomial(n+4, 4)/5 for n in (0..30)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..40], n-> (8*n+5)*Binomial(n+4, 4)/5); # G. C. Greubel, Aug 30 2019

Crossrefs

Cf. A000217, A001107, A051797.

Cf. A093565 ((8, 1) Pascal, column m=5).

Sequence in context: A285482 A175109 A265038 * A092653 A067465 A166605

Adjacent sequences: A051875 A051876 A051877 * A051879 A051880 A051881

Keyword

nonn,easy

Author

Barry E. Williams, Dec 14 1999

Extensions

Terms a(28) onward added by G. C. Greubel, Aug 30 2019

Status

approved