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Let j be the smallest integer for which 1+(1+1*n)+(1+2*n)+...+(1+j*n)=k^2=s. Then a(n)=s; if no such j exists, then a(n)=0.

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4

36, 4, 9801, 1225, 81, 225, 9, 0, 196, 64, 36, 441, 3025, 16, 17689, 100, 484, 0, 2601, 729, 68121, 225, 25, 7225, 25921, 81, 1225, 203401, 441, 1089, 4761, 196, 15376, 36, 1936, 511225, 784, 576, 55071241, 47089, 1156, 256, 529046001, 2916, 1134225 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Basis for sequence is shortest arithmetic series with initial term 1 and difference n that sums to a perfect square.`
	FORMULA	`1+(1+1n)+(1+2n)+...+(1+A100254(n)n)= 1+(1+1n)+(1+2*n)+...+A100253(n)=A100251(n)^2=a(n)`
	EXAMPLE	`a(3)=9801 since 1 + 4 + 7 +...+ (1+80*3)= 99^2 = 9801 and no other arithmetic series with initial term 1, difference 3 and fewer terms sums to a perfect square.`
	CROSSREFS	`Sequence in context: A013557 A022071 A037935 this_sequence A020340 A109256 A066583` `Adjacent sequences: A100249 A100250 A100251 this_sequence A100253 A100254 A100255`
	KEYWORD	`nonn`
	AUTHOR	`Charlie Marion (charliemath(AT)optonline.net), Nov 21 2004`

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Last modified July 24 12:00 EDT 2008. Contains 142294 sequences.

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