OFFSET
0,3
COMMENTS
5-dimensional form of octagonal-based pyramidal numbers. - Derek I. Thomas (dithom02(AT)louisville.edu), Jun 30 2007
Convolution of triangular numbers (A000217) and octagonal numbers (A000567). [Bruno Berselli, Jul 21 2015]
Also the number of 4-cycles in the (n+2)-triangular honeycomb bishop graph. - Eric W. Weisstein, Aug 10 2017
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
H. J. Ryser, Combinatorial Mathematics, Carus Mathematical Monographs No. 14, John Wiley and Sons, 1963, pp. 1-8.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Luis Verde-Star, A Matrix Approach to Generalized Delannoy and Schröder Arrays, J. Int. Seq., Vol. 24 (2021), Article 21.4.1.
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Octagonal Number
Eric Weisstein's World of Mathematics, Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = C(n+3,4) * (6*n-1)/5
G.f.: x*(1+5*x)/(1-x)^6.
a(n) = n*(n+1)*(n+2)*(n+3)*(6n-1)/120. - Derek I. Thomas (dithom02(AT)louisville.edu), Jun 30 2007
MATHEMATICA
Join[{0}, Accumulate[LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 40, 110, 245}, 40]]] (* Harvey P. Dale, Nov 30 2014 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 11, 51, 161, 406}, 40] (* Harvey P. Dale, Nov 30 2014 *)
Table[(6 n - 1) Binomial[n + 3, 4]/5, {n, 0, 20}] (* Eric W. Weisstein, Aug 10 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Dec 13 1999
EXTENSIONS
a(1) corrected by Gael Linder (linder.gael(AT)wanadoo.fr), Oct 31 2007
a(0) prepended by Joerg Arndt, Jun 26 2013
STATUS
approved