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A051878 Partial sums of A051797. 3
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 (list; graph; refs; listen; history; text; internal format)
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..27.

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) = C(n+4, 4)*(8n+5)/5.

G.f.: (1+7*x)/(1-x)^6.

MATHEMATICA

s=c=0; Table[c+=s+=n(n+1)(8n-5)/6, {n, 80}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)

CROSSREFS

Cf. A051797; A000217, A001107.

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

STATUS

approved

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Last modified February 25 08:45 EST 2018. Contains 299647 sequences. (Running on oeis4.)