A051843 Partial sums of A002419.
0, 1, 11, 51, 161, 406, 882, 1722, 3102, 5247, 8437, 13013, 19383, 28028, 39508, 54468, 73644, 97869, 128079, 165319, 210749, 265650, 331430, 409630, 501930, 610155, 736281, 882441, 1050931, 1244216, 1464936, 1715912, 2000152, 2320857, 2681427
Offset: 0
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 to sequences related to pyramidal numbers
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Crossrefs
Programs
-
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 *)
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
Extensions
a(1) corrected by Gael Linder (linder.gael(AT)wanadoo.fr), Oct 31 2007
a(0) prepended by Joerg Arndt, Jun 26 2013
Comments