A213948 - OEIS

A213948

Triangle, by rows, generated from the INVERT transforms of (1, 1, 2, 4, 8, 16, ...).

1, 1, 1, 1, 2, 2, 1, 4, 4, 4, 1, 7, 10, 8, 8, 1, 12, 24, 20, 16, 16, 1, 20, 52, 56, 40, 32, 32, 1, 33, 112, 144, 112, 80, 64, 64, 1, 54, 238, 344, 320, 224, 160, 128, 128, 1, 88, 496, 828, 848, 640, 448, 320, 256, 256

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OFFSET

1,5

COMMENTS

Row sums = A001519, the odd-indexed Fibonacci terms. The triangle is a companion to A213947, having row sums of the even-indexed Fibonacci terms.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Create an array in which the n-th row is the INVERT transform of the first n terms in the sequence (1, 1, 2, 4, 8, 16, 32, ...):

1, 1, 1, 1, 1, 1,

1, 2, 3, 5, 8, 13, (essentially A000045)

1, 2, 5, 9, 18, 37, (essentially A077947)

1, 2, 5, 13, 26, 57,

Terms of the n-th row of the triangle are the finite differences downwards the n-th column of this array.

EXAMPLE

First few rows of the triangle are:

1, 1;

1, 2, 2;

1, 4, 4, 4;

1, 7, 20, 8, 8;

1, 12, 24, 20, 16, 16;

1, 20, 52, 56, 40, 32, 32;

1, 33, 112, 144, 112, 80, 64, 64;

1, 54, 238, 344, 320, 224, 160, 128, 128;

1, 88, 496, 828, 848, 640, 448, 320, 256, 256;

...

MAPLE

read("transforms") ;

A213948i := proc(n, k)

if n = 1 then

L := [1, seq(0, i=0..k)] ;

else

L := [1, seq(2^i, i=0..n-2), seq(0, i=0..k)] ;

end if;

INVERT(L) ;

op(k, %) ;

end proc:

A213948 := proc(n, k)

if k = 1 then

else

A213948i(k, n)-A213948i(k-1, n) ;

end if;

end proc: # R. J. Mathar, Jun 30 2012

CROSSREFS

Cf. A001519, A213947, A000071 (2nd column), A020714 (subdiagonal), A005009 (subdiagonal).

Sequence in context: A319534 A061436 A214095 * A136787 A165038 A305191

Adjacent sequences: A213945 A213946 A213947 * A213949 A213950 A213951

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 25 2012

STATUS

approved