The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A134519 Numbers remaining when the natural numbers (A000027) are arranged into a triangle and only the beginning and end terms of each row are retained. 4
 1, 2, 3, 4, 6, 7, 10, 11, 15, 16, 21, 22, 28, 29, 36, 37, 45, 46, 55, 56, 66, 67, 78, 79, 91, 92, 105, 106, 120, 121, 136, 137, 153, 154, 171, 172, 190, 191, 210, 211, 231, 232, 253, 254, 276, 277, 300, 301, 325, 326, 351, 352, 378, 379, 406, 407, 435, 436, 465, 466 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, this is TriRet(A000027,{1}) = TriRem(A000027,{2,3,4,...}), using the operations defined in A134509. Bisections are A000217-{0} and A000124-{1}. A055802 and A114220 appear to be this sequence with two and three additional leading terms, respectively. LINKS Muniru A Asiru, Table of n, a(n) for n = 1..10000 Bruno Berselli, An interpretation of initial terms. FORMULA From Colin Barker, Jul 17 2013: (Start) a(n) = (16 + 4*n + 2*n^2)/16 for n even, a(n) = (3 + 4*n + n^2)/8 for n odd. G.f.: -x*(x^4 - x^3 - x^2 + x + 1) / ((x - 1)^3*(x + 1)^2). (End) a(n) = Sum_{k=0..n-1} A057979(k). - Jon Maiga, Dec 21 2018 a(n) = A000217(floor(n+1)/2) + (1 + (-1)^n)/2. - Bruno Berselli, Aug 20 2019 MAPLE seq(coeff(series(-x*(x^4-x^3-x^2+x+1)/((x-1)^3*(x+1)^2), x, n+1), x, n), n = 1 .. 60); # Muniru A Asiru, Dec 21 2018 MATHEMATICA Table[Sum[If[EvenQ[k], 1, (k - 1)/2], {k, 0, n}], {n, 60}] (* Jon Maiga, Dec 21 2018 *) PROG (GAP) a:=[];; for n in [1..60] do if n mod 2=0 then Add(a, (16+4*n+2*n^2)/16); else Add(a, (3+4*n+n^2)/8); fi; od; a; # Muniru A Asiru, Dec 21 2018 (MAGMA) T:=func; [T(Floor((n+1)/2))+(1+(-1)^n)/2: n in [1..60]]; // Bruno Berselli, Aug 20 2019 CROSSREFS Cf. A000027, A000124, A000217, A055802, A057979, A114220, A134509. Cf. A084263: A000217(m) + (1 + (-1)^m)/2. Cf. A117142: A000217(floor(m/2)+1) - (1 + (-1)^m)/2. Sequence in context: A294848 A055802 A114220 * A101505 A259625 A068713 Adjacent sequences:  A134516 A134517 A134518 * A134520 A134521 A134522 KEYWORD nonn,easy AUTHOR Rick L. Shepherd, Oct 29 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)