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A195026
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a(n) = 7*n*(2*n + 1).
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4
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0, 21, 70, 147, 252, 385, 546, 735, 952, 1197, 1470, 1771, 2100, 2457, 2842, 3255, 3696, 4165, 4662, 5187, 5740, 6321, 6930, 7567, 8232, 8925, 9646, 10395, 11172, 11977, 12810, 13671, 14560, 15477, 16422, 17395, 18396, 19425, 20482, 21567, 22680, 23821, 24990
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 0, in the direction 0, 21,..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020. Semi-diagonal opposite to A195320 in the same square spiral, which is related to the primitive Pythagorean triple [3, 4, 5].
Sum of the numbers from 6n to 8n. - Wesley Ivan Hurt, Dec 23 2015
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 14*n^2 + 7*n.
a(n) = 7*A014105(n). - Bruno Berselli, Oct 13 2011
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
G.f.: 7*x*(3+x)/(1-x)^3. (End)
a(n) = Sum_{i=6n..8n} i. - Wesley Ivan Hurt, Dec 23 2015
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MAPLE
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A195026:=n->7*n*(2*n+1): seq(A195026(n), n=0..50); # Wesley Ivan Hurt, Dec 23 2015
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MATHEMATICA
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Table[7*n*(2*n + 1), {n, 0, 50}] (* Wesley Ivan Hurt, Dec 23 2015 *)
LinearRecurrence[{3, -3, 1}, {0, 21, 70}, 50] (* Harvey P. Dale, Apr 26 2017 *)
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PROG
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(MAGMA) [14*n^2 +7*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011
(PARI) a(n)=7*n*(2*n+1) \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A014105, A144555, A152760, A195019, A195020, A195021, A195023, A195024, A195025, A195320.
Cf. A185019, A193053, A198017.
Sequence in context: A200931 A044159 A044540 * A296035 A102233 A309903
Adjacent sequences: A195023 A195024 A195025 * A195027 A195028 A195029
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KEYWORD
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nonn,easy
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AUTHOR
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Omar E. Pol, Oct 13 2011
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STATUS
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approved
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