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A035677 Number of partitions of n into parts 8k and 8k + 6 with at least one part of each type. 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 3, 0, 6, 0, 1, 0, 3, 0, 7, 0, 12, 0, 3, 0, 7, 0, 15, 0, 21, 0, 7, 0, 16, 0, 28, 0, 36, 0, 16, 0, 31, 0, 50, 0, 60, 0, 32, 0, 57, 0, 85, 0, 98, 0, 60, 0, 100, 0, 141, 0, 157, 0, 107, 0, 169, 0, 226, 0, 248, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,22

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..361

PROG

(PARI)

parts8katleast(up_to, n) = select(x -> (x>=n), vector(((up_to+0)>>3), k, ((k<<3)-0)));

parts8kplus6(up_to) = vector(((up_to+2)>>3), k, ((k<<3)-2));

partitions_for_A035677(n, parts, from=1, has8k6parts=0) = if(!n, (has8k6parts>0), my(k = #parts, s=0); for(i=from, k, if(parts[i]<=n, s += partitions_for_A035677(n-parts[i], parts, i, (has8k6parts+(6==(parts[i]%8)))))); (s));

A035677(n) = if(n%2, 0, sum(i=1, n>>3, my(k = i*8); partitions_for_A035677(n-k, vecsort(setunion(parts8katleast(n-k, k), parts8kplus6(n-k)), , 4)))); \\ Antti Karttunen, Feb 06 2019

CROSSREFS

Sequence in context: A193139 A083206 A069531 * A143276 A283470 A101941

Adjacent sequences:  A035674 A035675 A035676 * A035678 A035679 A035680

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)