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A201088 T(n,k)=Number of -k..k arrays of n elements with first and second differences also in -k..k.

%I A201088 #7 Jul 22 2025 16:04:56
%S A201088 3,5,7,7,19,13,9,37,57,25,11,61,153,175,47,13,91,323,651,537,89,15,
%T A201088 127,587,1759,2771,1653,169,17,169,967,3899,9593,11817,5089,321,19,
%U A201088 217,1483,7581,25935,52401,50391,15663,609,21,271,2157,13405,59533,172767,286207
%N A201088 T(n,k)=Number of -k..k arrays of n elements with first and second differences also in -k..k.
%C A201088 Table starts
%C A201088 ....3......5.......7........9........11.........13.........15..........17
%C A201088 ....7.....19......37.......61........91........127........169.........217
%C A201088 ...13.....57.....153......323.......587........967.......1483........2157
%C A201088 ...25....175.....651.....1759......3899.......7581......13405.......22085
%C A201088 ...47....537....2771.....9593.....25935......59533.....121371......226521
%C A201088 ...89...1653...11817....52401....172767.....468159....1100401.....2326467
%C A201088 ..169...5089...50391...286207...1150785....3681179....9975741....23891417
%C A201088 ..321..15663..214867..1563111...7664735...28943479...90429601...245334347
%C A201088 ..609..48207..916173..8536807..51049977..227567727..819732439..2519249143
%C A201088 .1155.148375.3906507.46623423.340013811.1789258703.7430807385.25869394013
%H A201088 R. H. Hardin, <a href="/A201088/b201088.txt">Table of n, a(n) for n = 1..9999</a>
%e A201088 Some solutions for n=4 k=7
%e A201088 ..2....2....4...-3....0....2....6....5...-2...-7...-7....4....3...-1...-3...-4
%e A201088 ..3....1....6...-5....5...-2....5....2...-1....0...-1...-1....1....0....3...-4
%e A201088 ..0....1....2...-3....3....1....3...-4....3....0...-2...-2...-1....1....4...-2
%e A201088 ..3...-5...-3....3...-2....4....1...-3....4....2...-6...-3....1....0....2....5
%Y A201088 Row 1 is A004273(n+1)
%Y A201088 Row 2 is A003215
%Y A201088 Row 3 is A007202
%K A201088 nonn,tabl
%O A201088 1,1
%A A201088 _R. H. Hardin_ Nov 26 2011