



1, 14, 60, 170, 385, 756, 1344, 2220, 3465, 5170, 7436, 10374, 14105, 18760, 24480, 31416, 39729, 49590, 61180, 74690, 90321, 108284, 128800, 152100, 178425, 208026, 241164, 278110, 319145, 364560, 414656, 469744, 530145, 596190
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

4dimensional pyramidal number, composed of consecutive 3dimensional slices; each of which is a 3dimensional 12gonal (or dodecagonal) pyramidal number; which in turn is composed of consecutive 2dimensional slices 12gonal numbers.  Jonathan Vos Post, Mar 17 2006
Convolution of A000027 with A051624 (excluding 0).  Bruno Berselli, Dec 07 2012


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 18.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGrawHill, 1971, pp. 1020, 7994.


LINKS

Table of n, a(n) for n=0..33.
Index to sequences related to pyramidal numbers
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

a(n) = C(n+3, 3)*(5*n+2)/2 = (n+1)*(n+2)*(n+3)*(5*n+2)/12.
G.f.: (1+9*x)/(1x)^5.


MATHEMATICA

Accumulate[Table[n(n+1)(10n7)/6, {n, 0, 50}]] (* Harvey P. Dale, Nov 13 2013 *)


PROG

(MAGMA) /* A000027 convolved with A051624 (excluding 0): */ A051624:=func<n  n*(5*n4)>; [&+[(ni+1)*A051624(i): i in [1..n]]: n in [1..35]]; // Bruno Berselli, Dec 07 2012


CROSSREFS

Cf. A007587, A051624.
Cf. A093645 ((10, 1) Pascal, column m=4).
Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the kgonal numbers.
Sequence in context: A158058 A100171 A063492 * A164540 A140184 A264854
Adjacent sequences: A051796 A051797 A051798 * A051800 A051801 A051802


KEYWORD

nonn,easy


AUTHOR

Barry E. Williams, Dec 11 1999


STATUS

approved



