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 A227344 Triangle read by rows, partitions into distinct parts by perimeter. 5
 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 0, 7, 0, 0, 0, 0, 1, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 11, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 16, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 20, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The perimeter of a partition is the sum of all parts p that do not have two neighbors (that is, not both p-1 and p+1 are parts). Row sums are A000009. Column sums are A122129 (noted by Patrick Devlin). LINKS Joerg Arndt, Table of n, a(n) for n = 1..5050 EXAMPLE Triangle starts (dots for zeros): 01: 1 02: . 1 03: . . 2 04: . . . 2 05: . . . . 3 06: . . . 1 . 3 07: . . . . . . 5 08: . . . . . . . 6 09: . . . . . 1 . . 7 10: . . . . 1 . . . . 9 11: . . . . . . . . 1 . 11 12: . . . . . . . 1 . 1 . 13 13: . . . . . . . . 1 . 1 . 16 14: . . . . . . 1 . . . . 1 . 20 15: . . . . . 1 . . . 1 . 1 1 . 23 16: . . . . . . . . . . 2 . 1 1 . 28 17: . . . . . . . . . . . 2 . 1 2 . 33 18: . . . . . . . . 1 . . 1 2 . 1 2 . 39 19: . . . . . . . . . 1 . . 1 1 1 1 3 . 46 20: . . . . . . . 1 . . . . . 1 1 2 1 3 . 55 21: . . . . . . 1 . . . . . . 2 2 1 2 1 4 . 63 22: . . . . . . . . . . 1 . 1 . 2 1 1 2 2 4 . 75 23: . . . . . . . . . . . 1 . 1 . 2 1 3 2 2 5 . 87 24: . . . . . . . . . . . . 1 . 1 2 3 . 4 2 3 5 . 101 25: . . . . . . . . . 1 . . . 1 . 1 1 3 . 6 2 3 7 . 117 26: . . . . . . . . . . 1 . 1 . . . 2 1 3 . 7 2 4 8 . 136 27: . . . . . . . . 1 . . . . 1 . . . 5 2 2 1 8 3 4 9 . 156 28: . . . . . . . 1 . . . . . . 1 1 . . 4 2 3 2 8 4 5 11 . 180 29: . . . . . . . . . . . . . . 1 2 1 . . 4 3 3 3 9 5 5 13 . 207 30: . . . . . . . . . . . 1 . . 1 1 1 1 . 3 6 2 2 5 9 6 6 14 . 238 MAPLE b:= proc(n, i, t) option remember; `if`(n=0, `if`(t>1, x^(i+1), 1),       expand(`if`(i<1, 0, `if`(t>1, x^(i+1), 1)*b(n, i-1, iquo(t, 2))+       `if`(i>n, 0, `if`(t=2, x^(i+1), 1)*b(n-i, i-1, iquo(t, 2)+2)))))     end: T:= n-> (p->seq(coeff(p, x, i), i=1..n))(b(n\$2, 0)): seq(T(n), n=1..20);  # Alois P. Heinz, Jul 16 2013 MATHEMATICA b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t>1, x^(i+1), 1], Expand[If[i<1, 0, If[t>1, x^(i+1), 1]*b[n, i-1, Quotient[t, 2]] + If[i>n, 0, If[t == 2, x^(i+1), 1]*b[n-i, i-1, Quotient[t, 2]+2]]]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, i], {i, 1, n}]][b[n, n, 0]]; Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Jan 28 2015, after Alois P. Heinz *) CROSSREFS Cf. A227345 (partitions by boundary size). Cf. A227426 (diagonal: number of partitions with maximal perimeter). Cf. A227538 (smallest k with positive T(n,k)), A227614 (second lower diagonal). - Alois P. Heinz, Jul 17 2013 Sequence in context: A325668 A070202 A280129 * A130207 A325433 A167688 Adjacent sequences:  A227341 A227342 A227343 * A227345 A227346 A227347 KEYWORD nonn,tabl AUTHOR Joerg Arndt, Jul 08 2013 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)