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Search: id:A131770
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| A131770 |
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First differences (A131771) equal this sequence with terms repeated at positions: {m*(m+1)/2, m>=0}. |
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+0
5
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| 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; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = a(n-1) + a(n - t(n)) where t(n) = [(sqrt(8n + 17) - 3)/2] for n>0, with a(0)=1.
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EXAMPLE
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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}.
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PROGRAM
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(PARI) a(n)=if(n==0, 1, a(n-1)+a(n-(sqrtint(8*n+17)-3)\2))
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CROSSREFS
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Cf. A131771 (first differences), A131772.
Adjacent sequences: A131767 A131768 A131769 this_sequence A131771 A131772 A131773
Sequence in context: A023598 A103258 A100684 this_sequence A163489 A076651 A081410
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 14 2007
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