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A131770 First differences (A131771) equal this sequence with terms repeated at positions: {m*(m+1)/2, m>=0}. 4
1, 2, 4, 8, 12, 20, 32, 52, 72, 104, 156, 228, 332, 436, 592, 820, 1152, 1588, 2180, 2772, 3592, 4744, 6332, 8512, 11284, 14876, 18468, 23212, 29544, 38056, 49340, 64216, 82684, 105896, 129108, 158652, 196708, 246048, 310264, 392948, 498844, 627952 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..41.

FORMULA

a(n) = a(n-1) + a(n - t(n)) where t(n) = [(sqrt(8n + 17) - 3)/2] for n>0, with a(0)=1.

EXAMPLE

First differences (A131771) begin:

[1,1,2,4,4,8,12,20,20,32,52,72,104,104,156,228,332,436,592,592,...].

Second differences (A131772) begin:

[1,0,1,2,0,4,4,8,0,12,20,20,32,0,52,72,104,104,156,0,228,332,436,592,592,...]

which equals the first differences with zeros inserted at positions {m*(m+1)/2, m>=0}.

PROG

(PARI) a(n)=if(n==0, 1, a(n-1)+a(n-(sqrtint(8*n+17)-3)\2))

CROSSREFS

Cf. A131771 (first differences), A131772.

Sequence in context: A307732 A103258 A100684 * A322419 A246850 A294066

Adjacent sequences:  A131767 A131768 A131769 * A131771 A131772 A131773

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 14 2007

STATUS

approved

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)