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A143839
Ulam's spiral (SSE spoke).
4
1, 24, 79, 166, 285, 436, 619, 834, 1081, 1360, 1671, 2014, 2389, 2796, 3235, 3706, 4209, 4744, 5311, 5910, 6541, 7204, 7899, 8626, 9385, 10176, 10999, 11854, 12741, 13660, 14611, 15594, 16609, 17656, 18735, 19846, 20989, 22164, 23371, 24610
OFFSET
1,2
COMMENTS
Also sequence found by reading the line from 1, in the direction 1, 24, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 05 2012
FORMULA
a(n) = 16*n^2 - 25*n + 10. - R. J. Mathar, Sep 04 2008
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1) = 1, a(2) = 24, a(3) = 79. - Harvey P. Dale, May 26 2012
G.f.: x*(1 + 21*x + 10*x^2)/(1-x)^3. - Harvey P. Dale, May 26 2012
E.g.f.: exp(x)*(10 - 9*x + 16*x^2) - 9. - Stefano Spezia, Oct 07 2019
MAPLE
seq( ((32*n -25)^2 +15)/64, n=1..40); # G. C. Greubel, Nov 09 2019
MATHEMATICA
f[n_] := 16n^2 -25n +10; Array[f, 40] (* Vladimir Joseph Stephan Orlovsky, Sep 02 2008 *)
LinearRecurrence[{3, -3, 1}, {1, 24, 79}, 40] (* Harvey P. Dale, May 26 2012 *)
CoefficientList[Series[(1+21*x+10*x^2)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Nov 08 2014 *)
PROG
(Magma) [16*n^2-25*n+10: n in [1..40]]; // Vincenzo Librandi, Nov 08 2014
(PARI) Vec(x*(1+21*x+10*x^2)/(1-x)^3 + O(x^40)) \\ Colin Barker, Nov 08 2014
(Sage) [((32*n -25)^2 +15)/64 for n in (1..40)] # G. C. Greubel, Nov 09 2019
(GAP) List([1..40], n-> ((32*n -25)^2 +15)/64); # G. C. Greubel, Nov 09 2019
CROSSREFS
Sequence in context: A206010 A124140 A206003 * A114818 A190102 A060673
KEYWORD
nonn,easy
AUTHOR
STATUS
approved