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A213948 Triangle, by rows, generated from the INVERT transforms of (1, 1, 2, 4, 8, 16, ...). 2
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 (list; table; graph; refs; listen; history; text; internal format)
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;

  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

        1;

    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

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Last modified January 20 02:46 EST 2021. Contains 340301 sequences. (Running on oeis4.)