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 A271508 Numbers that are congruent to {1,4} mod 10. 1
 1, 4, 11, 14, 21, 24, 31, 34, 41, 44, 51, 54, 61, 64, 71, 74, 81, 84, 91, 94, 101, 104, 111, 114, 121, 124, 131, 134, 141, 144, 151, 154, 161, 164, 171, 174, 181, 184, 191, 194, 201, 204, 211, 214, 221, 224, 231, 234, 241, 244, 251, 254, 261, 264, 271, 274 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers ending in 1 or 4, Union of A017281 and A017317. a(n+3) gives the sum of 5 consecutive terms of A004442 starting at A004442(n) for n>0. (i.e., a(4) = 14 = 0+3+2+5+4 = Sum_{i=0..4} A004442(n+i)). LINKS Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA G.f.: x*(1+3*x+6*x^2)/((-1+x)^2*(1+x)). a(n) = a(n-1) + a(n-2) - a(n-3) for n>3. a(n) = 5*n - 5 - (-1)^n. a(n) = -n + 2*A047241(n). a(n+1) = n + 1 + 2*A042948(n). Shifted bisections: a(2n+2) = A017317(n), a(2n+1) = A017281(n). E.g.f.: 5*(x-1)*exp(x) - exp(-x). - G. C. Greubel, Apr 08 2016 MAPLE A271508:=n->5*n-5-(-1)^n: seq(A271508(n), n=1..100); MATHEMATICA Table[5 n - 5 - (-1)^n, {n, 60}] (* or *) Select[Range[0, 300], MemberQ[{1, 4}, Mod[#, 10]] &] PROG (MAGMA) [5*n-5-(-1)^n : n in [1..100]]; (PARI) x='x+O('x^99); Vec(x*(1+3*x+6*x^2)/((-1+x)^2*(1+x))) \\ Altug Alkan, Apr 09 2016 CROSSREFS Cf. A004442, A017281, A017317, A042948, A047241. Sequence in context: A247521 A285979 A299975 * A284323 A091436 A032822 Adjacent sequences:  A271505 A271506 A271507 * A271509 A271510 A271511 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 08 2016 STATUS approved

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Last modified January 22 02:06 EST 2019. Contains 319351 sequences. (Running on oeis4.)