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Search: id:A106408
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| A106408 |
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Triangle, read by rows, where T(1,1) = 1; T(2,2) = 2; for n>2 T(n,n) = T(n-1,n-1) + T(n-2,n-2); T(n+1,n) = 2 * T(n,n); for all other entries T(n,k) = T(n-1,k) + T(n-2,k). |
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+0
2
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| 1, 2, 2, 3, 4, 3, 5, 6, 6, 5, 8, 10, 9, 10, 8, 13, 16, 15, 15, 16, 13, 21, 26, 24, 25, 24, 26, 21, 34, 42, 39, 40, 40, 39, 42, 34, 55, 68, 63, 65, 64, 65, 63, 68, 55, 89, 110, 102, 105, 104, 104, 105, 102, 110, 89, 144, 178, 165, 170, 168, 169, 168, 170, 165, 178, 144
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are A004798 (convolution of Fibonacci numbers 1,2,3,5,... with themselves). Central numbers of the rows are A006498 (a(n) = a(n-1)+a(n-3)+a(n-4)). First column and main diagonal are FIbonacci numbers 1,2,3,5,... First subdiagonal are 2*Fibonacci numbers. T(n,k) = F(n-k+2)*F(k+1) where F(m) is the m-th Fibonacci number. For the antidiagonal sums b(n): b(1) = 1, b(2) = 2, then b(n) = b(n-1) + b(n-2) + F(floor((n+3)/2)).
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FORMULA
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G.f.: (1+x+y+x*y)/((1-x-x^2)*(1-y-y^2)) [U coordinates] - njas, Jun 01 2005
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CROSSREFS
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Cf. A000045, A004798, A006498.
Sequence in context: A091524 A026350 A128282 this_sequence A096858 A037254 A071506
Adjacent sequences: A106405 A106406 A106407 this_sequence A106409 A106410 A106411
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KEYWORD
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nonn
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AUTHOR
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Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), May 28 2005
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