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A196700 Number of n X 1 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,0,4,2 for x=0,1,2,3,4. 6
1, 2, 4, 6, 12, 22, 40, 74, 136, 250, 460, 846, 1556, 2862, 5264, 9682, 17808, 32754, 60244, 110806, 203804, 374854, 689464, 1268122, 2332440, 4290026, 7890588, 14513054, 26693668, 49097310, 90304032, 166095010, 305496352, 561895394 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every 0 is next to zero 3's, every 1 is next to one 1, every 2 is next to two 0's, every 3 is next to three 4's, every 4 is next to four 2's.

Column 1 of A196707.

The perimeter of cuboids with the dimensions of consecutive tribonacci numbers, signature (0,1,0). - Peter M. Chema, Feb 03 2017

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) for n > 4.

G.f.: 1 - 1/x - 1/x^2 + 1/x^2/G(0), where G(k)= 1 - (2*k+1)*x/(1 - x/(x - (2*k+1)/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 09 2013

Empirical: a(n) = 2*(A001590(n) + A001590(n-1) + A001590(n-2)) for n > 1. - Peter M. Chema, Feb 03 2017

From Gregory L. Simay, Jun 23 2017: (Start)

a(n) = A000073(n+2) - A000073(n-2), the difference of two tribonacci numbers. The corresponding g.f. is (1 - x^4)/(1 - x - x^2 - x^3). E.g.: a(10) = A000073(12) - A000073(8) = 274 - 24 = 250.

The tribonacci formula arises from considering the number of compositions of n where only the order of parts 1,2,3 matters (part of an upcoming paper), which may be denoted by C(n [4). We are convolving the number of partitions of n with parts >3 with the tribonacci numbers. The number of partitions of n with parts greater than 3 is P(n) - P(n-1) - P(n-2) + P(n-4) + P(n-5) - P(n-6). (Derived from the corresponding gf which is (1-x)(1-x^2)(1-x^3)gfP(x).) The rest is algebra. It looks like C(n, [4) = P(n) + Sum_{j=0..n-3} P(n-3-j)*A196700(j+1). (End)

EXAMPLE

All solutions for n=4:

  0    0    1    0    0    0

  0    0    1    1    0    2

  1    0    0    1    2    0

  1    0    0    0    0    0

CROSSREFS

Cf. A000073, A001590, A196707.

Sequence in context: A005303 A292320 A057575 * A283834 A326114 A135231

Adjacent sequences:  A196697 A196698 A196699 * A196701 A196702 A196703

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 05 2011

STATUS

approved

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Last modified July 24 03:01 EDT 2019. Contains 325290 sequences. (Running on oeis4.)