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Search: id:A108356
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| A108356 |
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Count, repeating multiples of 3 four times, all other numbers twice. |
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+0
3
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| 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 28, 28, 29, 29, 30
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Diagonal sums of number triangle A108358. Partial sums of A108357.
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FORMULA
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G.f.: (1+x^2+x^4)/(1-x-x^8+x^9); a(n)=a(n-1)+a(n-8)-a(n-9); a(n)=sum{k=0..floor(n/2), mod(sum{j=0..n-2k, C(k, j)C(n-k-j, k)floor((j+2)/2)}, 2)}.
G.f.: (1-x^6)/((1-x)(1-x^2)(1-x^8)).
Euler transform of length 8 sequence [ 1, 1, 0, 0, 0, -1, 0, 1]. - Michael Somos Aug 31 2006
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, polcoeff( (x^4+x^2+1)/(x^9-x^8-x+1)+x*O(x^n), n))} /* Michael Somos Aug 31 2006 */
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CROSSREFS
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Sequence in context: A103264 A060960 A073642 this_sequence A055656 A078571 A071860
Adjacent sequences: A108353 A108354 A108355 this_sequence A108357 A108358 A108359
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 31 2005
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