The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A347808 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A347808

Expansion of (theta_3(x) - 1)^5 / (16 * (3 - theta_3(x))).
(history; published version)

#10 by Alois P. Heinz at Tue Sep 14 20:49:30 EDT 2021

STATUS

proposed

approved

#9 by Alois P. Heinz at Tue Sep 14 14:08:53 EDT 2021

STATUS

editing

proposed

#8 by Alois P. Heinz at Tue Sep 14 14:08:51 EDT 2021

MAPLE

b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0), add((

s->`if`(s>n, 0, b(n-s, max(0, t-1))))(j^2), j=1..isqrt(n)))

end:

a:= n-> b(n, 5):

seq(a(n), n=5..47); # Alois P. Heinz, Sep 14 2021

STATUS

proposed

editing

#7 by Alois P. Heinz at Tue Sep 14 13:41:07 EDT 2021

STATUS

editing

proposed

#6 by Alois P. Heinz at Tue Sep 14 13:41:05 EDT 2021

FORMULA

a(n) = Sum_{k=5..n} A337165(n,k). - Alois P. Heinz, Sep 14 2021

CROSSREFS

Cf. A000290, A006456, A337165, A347805, A347806, A347807, A347809.

STATUS

proposed

editing

#5 by Ilya Gutkovskiy at Tue Sep 14 12:18:33 EDT 2021

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Tue Sep 14 11:51:50 EDT 2021

CROSSREFS

Cf. A000290, A006456, A347805, A347806, A347807, A347809.

#3 by Ilya Gutkovskiy at Tue Sep 14 11:25:01 EDT 2021

CROSSREFS

Cf. A006456, A347805, A347806, A347807, A347809.

#2 by Ilya Gutkovskiy at Tue Sep 14 11:16:57 EDT 2021

NAME

allocated for Ilya Gutkovskiy

Expansion of (theta_3(x) - 1)^5 / (16 * (3 - theta_3(x))).

DATA

1, 1, 1, 6, 7, 8, 19, 25, 37, 56, 76, 122, 170, 233, 347, 494, 700, 991, 1415, 2021, 2855, 4054, 5751, 8164, 11585, 16406, 23285, 33032, 46814, 66375, 94119, 133445, 189193, 268231, 380287, 539184, 764422, 1083722, 1536479, 2178349, 3088333, 4378472, 6207557

OFFSET

5,4

COMMENTS

Number of compositions (ordered partitions) of n into 5 or more squares.

LINKS

<a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

MATHEMATICA

nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^5/(16 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 5] &

CROSSREFS

Cf. A006456.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Sep 14 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Tue Sep 14 11:16:57 EDT 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved