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 A195142 Concentric 10-gonal numbers. 14
 0, 1, 10, 21, 40, 61, 90, 121, 160, 201, 250, 301, 360, 421, 490, 561, 640, 721, 810, 901, 1000, 1101, 1210, 1321, 1440, 1561, 1690, 1821, 1960, 2101, 2250, 2401, 2560, 2721, 2890, 3061, 3240, 3421, 3610, 3801, 4000, 4201, 4410, 4621, 4840, 5061, 5290 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also concentric decagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 10, ..., and the same line from 1, in the direction 1, 21, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. Main axis, perpendicular to A028895 in the same spiral. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA G.f.: -x*(1+8*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011 a(n) = -a(n-1) + 5*n^2 - 5*n + 1, a(0)=0. - Vincenzo Librandi, Sep 27 2011 From Bruno Berselli, Sep 27 2011: (Start) a(n) = a(-n) = (10*n^2 + 3*(-1)^n - 3)/4. a(n) = a(n-2) + 10*(n-1). (End) a(n) = 2*a(n-1) + 0*a(n-2) - 2*a(n-3) + a(n-4); a(0)=0, a(1)=1, a(2)=10, a(3)=21. - Harvey P. Dale, Sep 29 2011 MATHEMATICA RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-2]+10(n-1)}, a[n], {n, 50}] (* or *) LinearRecurrence[{2, 0, -2, 1}, {0, 1, 10, 21}, 50] (* Harvey P. Dale, Sep 29 2011 *) PROG (MAGMA) [(10*n^2+3*(-1)^n-3)/4: n in [0..50]]; // Vincenzo Librandi, Sep 27 2011 (Haskell) a195142 n = a195142_list !! n a195142_list = scanl (+) 0 a090771_list -- Reinhard Zumkeller, Jan 07 2012 CROSSREFS Cf. A033583 and A069133 interleaved. Cf. A032527, A032528, A077221, A195042, A195143, A195145, A195146, A195147, A195148, A195149. Cf. A090771 (first differences). Column 10 of A195040. - Omar E. Pol, Sep 28 2011 Sequence in context: A324600 A240536 A060852 * A256884 A089584 A192743 Adjacent sequences:  A195139 A195140 A195141 * A195143 A195144 A195145 KEYWORD nonn,easy AUTHOR Omar E. Pol, Sep 17 2011 STATUS approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)