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A287276
Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= four.
4
1, 1, 2, 5, 15, 52, 188, 696, 2606, 9800, 36931, 139303, 525658, 1983925, 7488281, 28265353, 106692425, 402731694, 1520195297, 5738304135, 21660476556, 81762200416, 308629323572, 1164989004846, 4397506361848, 16599351862867, 62657893108843, 236515956134402
OFFSET
0,3
LINKS
Pierpaolo Natalini, Paolo Emilio Ricci, New Bell-Sheffer Polynomial Sets, Axioms 2018, 7(4), 71.
FORMULA
G.f.: -(x^7+x^5-6*x^4-x^2+4*x-1)/(x^8-x^7-7*x^5+7*x^4+x^3+4*x^2-5*x+1).
a(n) = A287214(n,4).
a(n) = A000110(n) for n <= 5.
EXAMPLE
a(6) = 188 = 203 - 15 = A000110(6) - 15 counts all set partitions of [6] except: 16|2345, 16|234|5, 16|235|4, 16|23|45, 16|23|4|5, 16|245|3, 16|24|35, 16|24|3|5, 16|25|34, 16|2|345, 16|2|34|5, 16|25|3|4, 16|2|35|4, 16|2|3|45, 16|2|3|4|5.
MATHEMATICA
LinearRecurrence[{5, -4, -1, -7, 7, 0, 1, -1}, {1, 1, 2, 5, 15, 52, 188, 696}, 30] (* Harvey P. Dale, Jan 02 2021 *)
CROSSREFS
Column k=4 of A287214.
Cf. A000110.
Sequence in context: A276721 A374329 A287583 * A361762 A367415 A369443
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, May 22 2017
STATUS
approved