A349523 - OEIS

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A349523

a(n) = Sum_{k=1..n} A339399(k).

1, 2, 3, 5, 6, 9, 11, 13, 14, 18, 20, 23, 24, 29, 31, 35, 38, 41, 42, 48, 50, 55, 58, 62, 63, 70, 72, 78, 81, 86, 90, 94, 95, 103, 105, 112, 115, 121, 125, 130, 131, 140, 142, 150, 153, 160, 164, 170, 175, 180, 181, 191, 193, 202, 205, 213, 217, 224, 229, 235, 236, 247, 249 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Partial sums of A339399.`
	LINKS	`Table of n, a(n) for n=1..63.` `Index entries for sequences related to partitions`
	FORMULA	`a(n) = Sum_{i=1..n} ((1+(-1)^i)(1+floor(sqrt(2i-1-(-1)^i)))/2-((2i+1-(-1)^i)/2-2 Sum_{k=1..floor(sqrt(2i-2-(-1)^i)-1)} floor((k+1)/2))(-1)^i/2).` `a(n) = Sum_{k=1..n} A339443(A103889(k)).`
	MATHEMATICA	`Table[Sum[((1 + (-1)^k) (1 + Floor[Sqrt[2 k - 1 - (-1)^k]])/2 - ((2 k + 1 - (-1)^k)/2 - 2 Sum[Floor[(i + 1)/2], {i, -1 + Floor[Sqrt[2 k - 2 - (-1)^k]]}]) (-1)^k/2), {k, n}], {n, 100}]`
	CROSSREFS	`Cf. A103889, A339399, A339443.` `Sequence in context: A284685 A113238 A104214 * A355616 A046657 A102825` `Adjacent sequences: A349520 A349521 A349522 * A349524 A349525 A349526`
	KEYWORD	`nonn`
	AUTHOR	`Wesley Ivan Hurt, Nov 20 2021`
	STATUS	`approved`

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Last modified March 25 13:31 EDT 2023. Contains 361524 sequences. (Running on oeis4.)