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Search: id:A081572
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| A081572 |
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Square array of binomial transforms of Fibonacci numbers, read by antidiagonals. |
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+0
2
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| 1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 10, 13, 5, 1, 5, 17, 35, 34, 8, 1, 6, 26, 75, 125, 89, 13, 1, 7, 37, 139, 338, 450, 233, 21, 1, 8, 50, 233, 757, 1541, 1625, 610, 34, 1, 9, 65, 363, 1490, 4172, 7069, 5875, 1597, 55, 1, 10, 82, 535, 2669, 9633, 23165, 32532, 21250, 4181, 89
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Rows include A000045, A001519, A081567, A081568, A081569, A081570, A081571 Rows are solutions of the recurrence a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2), a(0)=1,a(1)=k+1.
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FORMULA
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Rows are successive binomial transforms of F(n+1). T(n, k)=(1/2-sqrt(5)/10)((2k+1)/2-sqrt(5)/2)^n+(1/2+sqrt(5)/10)(sqrt(5)/2+(2k+1)/2)^n
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EXAMPLE
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The rows start
1 1 2 3 5 ...
1 2 5 13 34 ...
1 3 10 35 125 ...
1 4 17 75 338 ...
1 4 26 139 757 ...
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CROSSREFS
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Different from A073133.
Sequence in context: A038137 A073133 A106179 this_sequence A106196 A037027 A139375
Adjacent sequences: A081569 A081570 A081571 this_sequence A081573 A081574 A081575
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 22 2003
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