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A024966
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7 times triangular numbers.
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12
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0, 7, 21, 42, 70, 105, 147, 196, 252, 315, 385, 462, 546, 637, 735, 840, 952, 1071, 1197, 1330, 1470, 1617, 1771, 1932, 2100, 2275, 2457, 2646, 2842, 3045, 3255, 3472, 3696, 3927, 4165, 4410, 4662, 4921, 5187, 5460, 5740, 6027, 6321, 6622
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sequence found by reading the line from 0, in the direction 0, 7,... and the same line from 0, in the direction 1, 21,..., in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. This is the main diagonal in the spiral - Omar E. Pol, Sep 09 2011
Also sequence found by reading the same line mentioned above in the square spiral whose vertices are the generalized enneagonal numbers A118277. Axis perpendicular to A195145 in the same spiral. - Omar E. Pol, Sep 18 2011
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FORMULA
| a(n) = 7/2*n*(n+1). G.f.: A(x) = 7*x/(1-x)^3.
a(n) = (7n^2 + 7n)/2 = A000217(n)*7. - Omar E. Pol, Dec 12 2008
a(n) = a(n-1)+7*n (with a(0)=0). - Vincenzo Librandi, Nov 19 2010
a(n) = A069099(n+1) - 1. - Omar E. Pol, Oct 03 2011
a(n) = a(-n-1), a(n+2) = A193053(n+2)+2*A193053(n+1)+A193053(n). - Bruno Berselli, Oct 21 2011
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MAPLE
| [seq(7*binomial(n, 2), n=1..44)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 7!, 7}]; lst [From Vladimir Orlovsky, Nov 16 2008]
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CROSSREFS
| Cf. A028896, A033996.
Cf. A028895, A046092, A045943, A002378, A028896.
Cf. A000217. [From Omar E. Pol, Dec 12 2008]
Sequence in context: A024837 A205864 A162818 * A022602 A054569 A077354
Adjacent sequences: A024963 A024964 A024965 * A024967 A024968 A024969
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KEYWORD
| nonn,easy
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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