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Search: id:A131569
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| A131569 |
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a(n) = (1/2)*(F(n+2)-1)*(F(n+2)-2) + F(n), where F() are the Fibonacci numbers. |
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+0
1
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| 1, 2, 8, 24, 71, 198, 541, 1452, 3862, 10208, 26885, 70644, 185369, 485982, 1273420, 3335640, 8735707, 22875050, 59895221, 156819960, 410579786, 1074943872, 2814291433, 7367994504, 19289795761, 50501560538, 132215157296
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OFFSET
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1,2
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COMMENT
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Consider the infinite array M, containing the positive integers by antidiagonals from lower left to upper right: M(j,k) = (k+j-1)*(k+j)/2-(j-1); j, k >= 1. a(n) is the element in row F(n+1) and column F(n), i. e. a(n) = M(F(n+1),F(n)).
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EXAMPLE
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Upper left 6 X 6 submatrix of M is
[ 1 3 6 10 15 21]
[ 2 5 9 14 20 27]
[ 4 8 13 19 26 34]
[ 7 12 18 25 33 42]
[11 17 24 32 41 51]
[16 23 31 40 50 61]
F(0) through F(7) are 0, 1, 1, 2, 3, 5, 8, 13. a(4) = M(F(5),F(4)) = M(5,3) = 24.
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PROGRAM
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(PARI) for(n=1, 27, print1((1/2)*(fibonacci(n+2)-1)*(fibonacci(n+2)-2)+fibonacci(n), ", ")) /* Klaus Brockhaus, Aug 29 2007 */
(MAGMA) z:=15; m:=Fibonacci(z+1); M:=Matrix(IntegerRing(), m, m, [ [ (k+j-1)*(k+j)/2-(j-1): k in [1..m] ]: j in [1..m] ] ); [ M[Fibonacci(n+1), Fibonacci(n)]: n in [1..z] ] /* Klaus Brockhaus, Aug 29 2007 */
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CROSSREFS
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Cf. A000045 (Fibonacci numbers).
Sequence in context: A018045 A050242 A045697 this_sequence A066973 A130495 A026070
Adjacent sequences: A131566 A131567 A131568 this_sequence A131570 A131571 A131572
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Aug 27 2007
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 29 2007
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