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%I M4895
%S 0,1,13,46,110,215,371,588,876,1245,1705,2266,2938,3731,4655,5720,
%T 6936,8313,9861,11590,13510,15631,17963,20516,23300,26325,29601,33138,
%U 36946,41035,45415,50096,55088,60401,66045
%N 12-gonal (or dodecagonal) pyramidal numbers: n(n+1)(10n-7)/6.
%C Binomial transform of [1, 12, 21, 10, 0, 0, 0,...] = (1, 13, 46, 110,...). - _Gary W. Adamson_, Nov 28 2007
%C This sequence is related to A000566 by a(n) = n*A000566(n) - sum(A000566(i), i=0..n-1) and this is the case d=5 in the identity n*(n*(d*n-d+2)/2)-sum(k*(d*k-d+2)/2, k=0..n-1) = n*(n+1)*(2*d*n-2*d+3)/6. - Bruno Berselli, Oct 18 2010
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H B. Berselli, A description of the recursive method in Comments lines: website <a href="http://www.lanostra-matematica.org/2008/12/sequenze-numeriche-e-procedimenti.html">Matem@ticamente</a> (in Italian).
%F a(n) = (10*n-7)*binomial(n+1, 2)/3. G.f.: x*(1+9*x)/(1-x)^4.
%F a(n) = Sum_{k=0..n} k*(5*k-4). [From _Klaus Brockhaus_, Nov 20 2008]
%o (MAGMA) [ n eq 1 select 0 else Self(n-1)+(n-1)*(5*n-9): n in [1..35] ]; [From _Klaus Brockhaus_, Nov 20 2008]
%Y Cf. A093645 ((10, 1) Pascal, column m=3). Partial sums of A051624.
%Y Cf. A000566.
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_, R. K. Guy.
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