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A178534 Triangle T(n,k) read by rows. T(n,1)=A000045(n+1), k>1: T(n,k) = (sum from i = 1 to k-1 of T(n-i,k-1)) - (sum from i = 1 to k-1 of T(n-i,k)). 2
1, 2, 1, 3, 1, 1, 5, 2, 1, 1, 8, 3, 1, 1, 1, 13, 5, 3, 1, 1, 1, 21, 8, 4, 2, 1, 1, 1, 34, 13, 6, 4, 2, 1, 1, 1, 55, 21, 11, 6, 3, 2, 1, 1, 1, 89, 34, 17, 9, 6, 3, 2, 1, 1, 1, 144, 55, 27, 15, 9, 5, 3, 2, 1, 1, 1, 233, 89, 45, 25, 14, 9, 5, 3, 2, 1, 1, 1, 377, 144, 72, 40, 23, 14, 8, 5, 3, 2, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..91.

FORMULA

T(n,1)=A000045(n+1), k>1: T(n,k) = (sum from i = 1 to k-1 of T(n-i,k-1)) - (sum from i = 1 to k-1 of T(n-i,k)).

T(n,k)=A129713*A051731. [From Mats Granvik, Oct 22 2010]

EXAMPLE

Table begins:

1,

2,1,

3,1,1,

5,2,1,1,

8,3,1,1,1,

13,5,3,1,1,1,

21,8,4,2,1,1,1,

34,13,6,4,2,1,1,1,

55,21,11,6,3,2,1,1,1,

89,34,17,9,6,3,2,1,1,1,

PROG

(Excel) =if(column()=1; if(row()=1; 1; if(row()=2; 2; indirect(address(row()-1; 1))+indirect(address(row()-2; 1)))); if(row()>=column(); sum(indirect(address(row()-column()+1; column()-1; 4)&":"&address(row()-column()+column()-1; column()-1; 4); 4))-sum(indirect(address(row()-column()+1; column(); 4)&":"&address(row()-column()+column()-1; column(); 4); 4)); 0))

CROSSREFS

Cf. 1st column=A000045(n+1), 2nd=A000045, 3rd=A093040, 4th=A006498. Matrix inverse of A178535.

Sequence in context: A026807 A179045 A106740 * A110619 A191861 A129761

Adjacent sequences:  A178531 A178532 A178533 * A178535 A178536 A178537

KEYWORD

nonn,tabl

AUTHOR

Mats Granvik, May 29 2010

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.