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A286159 Lower triangular region of array A286156, transposed. 3
1, 1, 3, 1, 4, 6, 1, 4, 3, 10, 1, 4, 8, 7, 15, 1, 4, 8, 3, 6, 21, 1, 4, 8, 13, 7, 11, 28, 1, 4, 8, 13, 3, 12, 10, 36, 1, 4, 8, 13, 19, 7, 6, 16, 45, 1, 4, 8, 13, 19, 3, 12, 11, 15, 55, 1, 4, 8, 13, 19, 26, 7, 18, 17, 22, 66, 1, 4, 8, 13, 19, 26, 3, 12, 6, 10, 21, 78, 1, 4, 8, 13, 19, 26, 34, 7, 18, 11, 16, 29, 91, 1, 4, 8, 13, 19, 26, 34, 3, 12, 25, 17, 23, 28, 105 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle

EXAMPLE

The first ten rows of this triangular array:

  1,

  1, 3,

  1, 4, 6,

  1, 4, 3, 10,

  1, 4, 8,  7, 15,

  1, 4, 8,  3,  6, 21,

  1, 4, 8, 13,  7, 11, 28,

  1, 4, 8, 13,  3, 12, 10, 36,

  1, 4, 8, 13, 19,  7,  6, 16, 45,

  1, 4, 8, 13, 19,  3, 12, 11, 15, 55

MATHEMATICA

Map[((#1 + #2)^2 + 3 #1 + #2)/2 & @@ # & /@ Reverse@ # &, Table[Reverse@ QuotientRemainder[n, k], {n, 14}, {k, n}]] // Flatten (* Michael De Vlieger, May 20 2017 *)

PROG

(Scheme) (define (A286159 n) (A286156bi (A002024 n) (A004736 n))) ;; For A286156bi see A286156.

(Python)

def T(a, b): return ((a + b)**2 + 3*a + b)/2

def a(n, k): return T(n%k, int(n/k))

for n in range(1, 21): print [a(n , k) for k in range(1, n + 1)][::-1]  # Indranil Ghosh, May 20 2017

CROSSREFS

Transpose: A268158.

Cf. A000012, A000217, A268156, A268157.

Rows converge towards A034856.

Sequence in context: A116416 A051203 A243553 * A307394 A194540 A193043

Adjacent sequences:  A286156 A286157 A286158 * A286160 A286161 A286162

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved

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Last modified June 12 08:13 EDT 2021. Contains 344943 sequences. (Running on oeis4.)