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Search: id:A073372
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| A073372 |
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Second convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself. |
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+0
6
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| 1, 3, 12, 34, 99, 261, 678, 1692, 4149, 9959, 23568, 55014, 127031, 290457, 658602, 1482240, 3314025, 7365915, 16285300, 35832810, 78500811, 171293293, 372412782, 806963364, 1743173469, 3754782351
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n)=sum(b(k)*c(n-k), k=0..n) with b(k) := A001045(k+1) and c(k) := A073371(k).
a(n)=sum(binomial(n-k+2, 2)*binomial(n-k, k)*2^k, k=0..floor(n/2)).
a(n)= ((30+9*n)*(n+1)*U(n+1)+2*(33+9*n)*(n+2)*U(n))/(2*9^2) with U(n) := A001045(n+1), n>=0.
G.f.: 1/(1-(1+2*x)*x)^3.
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CROSSREFS
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Third (m=2) column of triangle A073370.
Adjacent sequences: A073369 A073370 A073371 this_sequence A073373 A073374 A073375
Sequence in context: A117655 A081423 A060298 this_sequence A026573 A097339 A009787
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 2002
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