A180352 A permutation of Motzkin numbers by reversal of indices in blocks of length 7.

127, 51, 21, 9, 4, 2, 1, 113634, 41835, 15511, 5798, 2188, 835, 323, 142547559, 50852019, 18199284, 6536382, 2356779, 853467, 310572, 208023278209, 73007772802, 25669818476, 9043402501, 3192727797, 1129760415, 400763223

Offset: 1

Author

Matt Insall (insall(AT)mst.edu), Aug 29 2010

Keywords

• less
• easy
• nonn

Comments

The sequence shows A001006(7) down to A001006(1), then A001006(14) down to A001006(8), etc., varying the index in a sawtooth pattern.

When I initially logged in to use the OEIS, it 'pre-loaded' the search box with a sequence. The seven terms 127,51,21,9,4,2,1 are obtained from that original one by reversing the terms.

"Periodic" term reversals of this sort are routinely encountered when writing out convolution sums.

Crossrefs

Cf. A001006, A073794

Programs

Sage

A180352 = lambda n: A001006(7*((n-1)//7+1)-((n-1) % 7)) # D. S. McNeil, Dec 06 2010

Formula

Let r(n) = 7, 6, 5 ,4, 3, 2, 1 (n>=1), extended with r(n+7)=7+r(n), then a(n) = A001006(r(n)).