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%I #29 Apr 21 2018 10:15:05
%S 1,15,91,325,861,1891,3655,6441,10585,16471,24531,35245,49141,66795,
%T 88831,115921,148785,188191,234955,289941,354061,428275,513591,611065,
%U 721801,846951,987715,1145341,1321125,1516411,1732591,1971105,2233441,2521135,2835771,3178981,3552445,3957891,4397095,4871881
%N Pyramidal centered square numbers.
%C a(n) is sum of natural numbers filled in order-n diamond.
%C First differences give A173962.
%H Colin Barker, <a href="/A237516/b237516.txt">Table of n, a(n) for n = 1..1000</a>
%H Kival Ngaokrajang, <a href="/A237516/a237516.pdf">Illustration for n = 1..6</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Diamond.html">Diamond</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 2n^4 - 4n^3 + 5n^2 - 3n + 1.
%F a(n) = Sum_{i = 1..(2n(n + 1) + 1)} i.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Colin Barker_, Jan 17 2015
%F G.f.: -x*(x^2+4*x+1)*(x^2+6*x+1) / (x-1)^5. - _Colin Barker_, Jan 17 2015
%F a(n) = A000217(A001844(n-1)). - _Ivan N. Ianakiev_, Jun 14 2015
%F a(n) = A002061(n) * A001844(n-1). - _Bruce J. Nicholson_, May 14 2017
%t Table[Sum[i, {i, 2n(n + 1) + 1}], {n, 0, 29}] (* _Alonso del Arte_, Feb 09 2014 *)
%t LinearRecurrence[{5,-10,10,-5,1},{1,15,91,325,861},60] (* _Harvey P. Dale_, Apr 21 2018 *)
%o (Small Basic)
%o For n = 0 to 50
%o a = 0
%o For n1 = 1 to 2*n*(n+1)+1
%o a = a + n1
%o EndFor
%o TextWindow.Write(a+", ")
%o EndFor
%o (PARI) Vec(-x*(x^2+4*x+1)*(x^2+6*x+1)/(x-1)^5 + O(x^100)) \\ _Colin Barker_, Jan 17 2015
%Y Cf. A001844, A173962.
%Y Cf. A002061, A000217.
%K nonn,easy
%O 1,2
%A _Kival Ngaokrajang_, Feb 08 2014
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