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A226252 Number of ways of writing n as the sum of 7 triangular numbers. 17

%I #22 Aug 01 2017 11:50:23

%S 1,7,21,42,77,126,175,253,357,434,567,735,833,1057,1302,1400,1708,

%T 2037,2191,2597,3003,3151,3619,4242,4389,4935,5691,5740,6594,7434,

%U 7371,8400,9303,9506,10626,11592,11585,12761,14427,14203,15519,17241,16808,18788,20559,19950,21882,23898,23786

%N Number of ways of writing n as the sum of 7 triangular numbers.

%H Seiichi Manyama, <a href="/A226252/b226252.txt">Table of n, a(n) for n = 0..10000</a>

%H K. Ono, S. Robins and P. T. Wahl, <a href="http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/006.pdf">On the representation of integers as sums of triangular numbers</a>, Aequationes mathematicae, August 1995, Volume 50, Issue 1-2, pp 73-94.

%F G.f. is 7th power of g.f. for A010054.

%F a(0) = 1, a(n) = (7/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - _Seiichi Manyama_, May 06 2017

%F G.f.: exp(Sum_{k>=1} 7*(x^k/k)/(1 + x^k)). - _Ilya Gutkovskiy_, Jul 31 2017

%Y Number of ways of writing n as a sum of k triangular numbers, for k=1,...: A010054, A008441, A008443, A008438, A008439, A008440, A226252, A007331, A226253, A226254, A226255, A014787, A014809.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jun 01 2013

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