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A319435 Number of partitions of n^2 into exactly n nonzero squares. 5
1, 1, 0, 1, 1, 1, 4, 4, 9, 16, 24, 52, 83, 152, 305, 515, 959, 1773, 3105, 5724, 10255, 18056, 32584, 58082, 101719, 179306, 317610, 552730, 962134, 1683435, 2899064, 4995588, 8638919, 14746755, 25196684, 43082429, 72959433, 123554195, 209017908, 351164162 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) = A243148(n^2,n).

EXAMPLE

a(0) = 1: the empty partition.

a(1) = 1: 1.

a(2) = 0: there is no partition of 4 into exactly 2 nonzero squares.

a(3) = 1: 441.

a(4) = 1: 4444.

a(5) = 1: 94444.

a(6) = 4: (25)44111, (16)(16)1111, (16)44444, 999441.

a(7) = 4: (25)(16)41111, (25)444444, (16)(16)44441, (16)999411.

a(8) = 9: (49)9111111, (36)(16)441111, (36)4444444, (25)(25)911111, (25)(16)944411, (25)9999111, (16)(16)(16)94111, (16)9999444, 99999991.

MAPLE

h:= proc(n) option remember; `if`(n<1, 0,

      `if`(issqr(n), n, h(n-1)))

    end:

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

      t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))

    end:

a:= n-> (s-> b(s$2, n)-`if`(n=0, 0, b(s$2, n-1)))(n^2):

seq(a(n), n=0..40);

CROSSREFS

Cf. A243148, A259254, A319503.

Sequence in context: A262811 A294749 A098359 * A226096 A071567 A304990

Adjacent sequences:  A319432 A319433 A319434 * A319436 A319437 A319438

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2018

STATUS

approved

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Last modified October 30 06:31 EDT 2020. Contains 338077 sequences. (Running on oeis4.)