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%I #37 Jun 11 2021 18:24:24
%S 0,1,11,51,161,406,882,1722,3102,5247,8437,13013,19383,28028,39508,
%T 54468,73644,97869,128079,165319,210749,265650,331430,409630,501930,
%U 610155,736281,882441,1050931,1244216,1464936,1715912,2000152,2320857,2681427
%N Partial sums of A002419.
%C 5-dimensional form of octagonal-based pyramidal numbers. - Derek I. Thomas (dithom02(AT)louisville.edu), Jun 30 2007
%C Convolution of triangular numbers (A000217) and octagonal numbers (A000567). [_Bruno Berselli_, Jul 21 2015]
%C Also the number of 4-cycles in the (n+2)-triangular honeycomb bishop graph. - _Eric W. Weisstein_, Aug 10 2017
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%D H. J. Ryser, Combinatorial Mathematics, Carus Mathematical Monographs No. 14, John Wiley and Sons, 1963, pp. 1-8.
%H Michael De Vlieger, <a href="/A051843/b051843.txt">Table of n, a(n) for n = 0..10000</a>
%H Luis Verde-Star <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Verde/verde4.html">A Matrix Approach to Generalized Delannoy and Schröder Arrays</a>, J. Int. Seq., Vol. 24 (2021), Article 21.4.1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = C(n+3,4) * (6*n-1)/5
%F G.f.: x*(1+5*x)/(1-x)^6.
%F a(n) = n*(n+1)*(n+2)*(n+3)*(6n-1)/120. - Derek I. Thomas (dithom02(AT)louisville.edu), Jun 30 2007
%t Join[{0}, Accumulate[LinearRecurrence[{5, -10, 10, -5, 1},{1, 10, 40, 110, 245}, 40]]] (* _Harvey P. Dale_, Nov 30 2014 *)
%t LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 11, 51, 161, 406}, 40] (* _Harvey P. Dale_, Nov 30 2014 *)
%t Table[(6 n - 1) Binomial[n + 3, 4]/5, {n, 0, 20}] (* _Eric W. Weisstein_, Aug 10 2017 *)
%Y Cf. A002419; A000217, A000567.
%Y Cf. A093563 ((6, 1) Pascal, column m=5).
%Y Cf. A034827 (3-cycles in the triangular honeycomb bishop graph), A290775 (5-cycles), A290779 (6-cycles).
%K easy,nonn
%O 0,3
%A _Barry E. Williams_, Dec 13 1999
%E a(1) corrected by Gael Linder (linder.gael(AT)wanadoo.fr), Oct 31 2007
%E a(0) prepended by _Joerg Arndt_, Jun 26 2013
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