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A303667 Expansion of 2/((1 - x)*(3 - theta_3(x))), where theta_3() is the Jacobi theta function. 4
1, 2, 3, 4, 6, 9, 13, 18, 25, 36, 52, 74, 104, 147, 209, 297, 421, 596, 845, 1199, 1701, 2411, 3417, 4844, 6868, 9738, 13806, 19573, 27749, 39342, 55778, 79079, 112112, 158944, 225342, 319479, 452941, 642152, 910404, 1290719, 1829911, 2594344, 3678108, 5214606, 7392970, 10481335 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A006456.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

FORMULA

G.f.: 1/((1 - x)*(1 - Sum_{k>=1} x^(k^2))).

MAPLE

b:= proc(n) option remember;

      `if`(n=0, 1, add(b(n-i^2), i=1..isqrt(n)))

    end:

a:= proc(n) option remember;

      `if`(n<0, 0, b(n)+a(n-1))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 28 2018

MATHEMATICA

nmax = 45; CoefficientList[Series[2/((1 - x) (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x]

nmax = 45; CoefficientList[Series[1/((1 - x) (1 - Sum[x^k^2, {k, 1, nmax}])), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[Boole[IntegerQ[k^(1/2)]] a[n - k], {k, 1, n}]; Accumulate[Table[a[n], {n, 0, 45}]]

CROSSREFS

Cf. A000290, A006456, A010052, A302833, A303668.

Sequence in context: A239551 A219282 A098578 * A050811 A076968 A238430

Adjacent sequences:  A303664 A303665 A303666 * A303668 A303669 A303670

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 28 2018

STATUS

approved

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Last modified August 4 08:20 EDT 2020. Contains 336201 sequences. (Running on oeis4.)