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A303909 Expansion of 2*(1 - x)/(3 - theta_3(x)), where theta_3() is the Jacobi theta function. 0
1, 0, 0, 0, 1, 1, 1, 1, 2, 4, 5, 6, 8, 13, 19, 26, 36, 51, 74, 105, 148, 208, 296, 421, 597, 846, 1198, 1699, 2409, 3417, 4843, 6865, 9732, 13799, 19566, 27739, 39325, 55749, 79041, 112063, 158877, 225241, 319331, 452734, 641866, 910001, 1290137, 1829079, 2593169, 3676457, 5212266 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

First differences of A006456.

LINKS

Table of n, a(n) for n=0..50.

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 - x)/(1 - Sum_{k>=1} x^(k^2)).

MAPLE

b:= proc(n) option remember; `if`(n<0, 0,

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

    end:

a:= n-> b(n)-`if`(n=0, 0, b(n-1)):

seq(a(n), n=0..60);  # Alois P. Heinz, May 02 2018

MATHEMATICA

nmax = 50; CoefficientList[Series[2 (1 - x)/(3 - EllipticTheta[3, 0, x]), {x, 0, nmax}], x]

nmax = 50; CoefficientList[Series[(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}]; Differences[Table[a[n], {n, -1, 50}]]

CROSSREFS

Cf. A000290, A006456, A078134, A303667.

Sequence in context: A245319 A037081 A270877 * A110277 A325680 A176654

Adjacent sequences:  A303906 A303907 A303908 * A303910 A303911 A303912

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 02 2018

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)